Twiddle factor generation

Abstract

Systems and methods for generating twiddle factors are described herein according to various embodiments of the present disclosure. In one embodiment, a method for twiddle factor generation comprises generating a first twiddle phase, wherein the first twiddle phase is from a set of radix-M1 twiddle phases, and M1 is an integer. The method also comprises converting the first twiddle phase into a second twiddle phase, wherein the second twiddle phase is from a set of radix-M2 twiddle phases, and M2 is an integer that is different from M1. The method further comprises generating a twiddle factor based on the second twiddle phase.

What is claimed is: 
     
         1 . A method for twiddle factor generation, comprising:
 generating a first twiddle phase, wherein the first twiddle phase is from a set of radix-M1 twiddle phases, and M1 is an integer;   converting the first twiddle phase into a second twiddle phase, wherein the second twiddle phase is from a set of radix-M2 twiddle phases, and M2 is an integer that is different from M1; and   generating a twiddle factor based on the second twiddle phase.   
     
     
         2 . The method of  claim 1 , wherein radix-M1 is one of radix-3 and radix-5, and radix-M2 is radix-2. 
     
     
         3 . The method of  claim 1 , wherein converting the first twiddle phase into the second twiddle phase comprises:
 multiplying the first twiddle phase by a phase ratio; and   rounding the multiplied twiddle phase to a nearest phase in the set of radix-M2 twiddle phases.   
     
     
         4 . The method of  claim 3 , wherein the phase ratio is a ratio of a number of phases in the set of radix-M2 twiddle phases over a number of phases in the set of radix-M1 twiddle phases. 
     
     
         5 . The method of  claim 1 , wherein generating the twiddle factor comprises inputting the second twiddle phase to a radix-M2 lookup table (LUT) device. 
     
     
         6 . The method of  claim 1 , wherein the twiddle factor is a complex number on a unit circle in a complex plane. 
     
     
         7 . The method of  claim 1 , further comprising:
 generating a third twiddle phase, wherein the third twiddle phase is from a set of radix-M3 twiddle phases, and M3 is an integer that is different from M1 and M2;   converting the third twiddle phase into a fourth twiddle phase, wherein the fourth twiddle phase is from the set of radix-M2 twiddle phases; and   generating a second twiddle factor based on the fourth twiddle phase.   
     
     
         8 . A twiddle factor generator, comprising:
 a twiddle phase generator configured to generate a first twiddle phase, wherein the first twiddle phase is from a set of radix-M1 twiddle phases, and M1 is an integer;   a phase converter configured to convert the first twiddle phase into a second twiddle phase, wherein the second twiddle phase is from a set of radix-M2 twiddle phases, and M2 is an integer that is different from M1; and   a lookup table (LUT) device configured to generate a twiddle factor based on the second twiddle phase.   
     
     
         9 . The twiddle factor generator of  claim 8 , wherein radix-M1 is one of radix-3 and radix-5, and radix-M2 is radix-2. 
     
     
         10 . The twiddle factor generator of  claim 8 , wherein the phase converter comprises:
 a multiplier configured to multiply the first twiddle phase by a phase ratio; and   a rounder configured to round the multiplied twiddle phase to a nearest phase in the set of radix-M2 twiddle phases.   
     
     
         11 . The twiddle factor generator of  claim 10 , wherein the phase ratio is a ratio of a number of phases in the set of radix-M2 twiddle phases over a number of phases in the set of radix-M1 twiddle phases. 
     
     
         13 . The twiddle factor generator of  claim 8 , further comprising:
 a second twiddle phase generator configured to generate a third twiddle phase, wherein the third twiddle phase is from a set of radix-M3 twiddle phases, and M3 is an integer that is different from M1 and M2;   wherein the phase converter is configured to convert the third twiddle phase into a fourth twiddle phase, wherein the fourth twiddle phase is from the set of radix-M2 twiddle phase, and the LUT device is configured to generate a second twiddle factor based on the fourth twiddle phase.   
     
     
         14 . The twiddle factor generator of  claim 13 , further comprising a multiplexer, wherein the multiplexer is configured to couple the first twiddle phase generator to the phase converter to generate the first twiddle factor, and to couple the second twiddle phase generator to the phase converter to generate the second twiddle factor. 
     
     
         15 . The twiddle factor generator of  claim 8 , wherein the twiddle phase generator, the phase converter, and the LUT device are implemented in hardware. 
     
     
         16 . A apparatus for twiddle factor generation, comprising:
 means for generating a first twiddle phase, wherein the first twiddle phase is from a set of radix-M1 twiddle phases, and M1 is an integer;   means for converting the first twiddle phase into a second twiddle phase, wherein the second twiddle phase is from a set of radix-M2 twiddle phases, and M2 is an integer that is different from M1; and   means for generating a twiddle factor based on the second twiddle phase.   
     
     
         17 . The apparatus of  claim 16 , wherein radix-M1 is one of radix-3 and radix-5, and radix-M2 is radix-2. 
     
     
         18 . The apparatus of  claim 16 , wherein the means for converting the first twiddle phase into the second twiddle phase comprises:
 means for multiplying the first twiddle phase by a phase ratio; and   means for rounding the multiplied twiddle phase to a nearest phase in the set of radix-M2 twiddle phases.   
     
     
         19 . The apparatus of  claim 18 , wherein the phase ratio is a ratio of a number of phases in the set of radix-M2 twiddle phases over a number of phases in the set of radix-M1 twiddle phases. 
     
     
         20 . The apparatus of  claim 16 , further comprising:
 means for generating a third twiddle phase, wherein the third twiddle phase is from a set of radix-M3 twiddle phases, and M3 is an integer that is different from M1 and M2;   means for converting the third twiddle phase into a fourth twiddle phase, wherein the fourth twiddle phase is from the set of radix-M2 twiddle phases; and   means for generating a second twiddle factor based on the fourth twiddle phase.